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Parsons gave a recursive formula to determine the values of $R(P_n,K_{1,m})$, where $P_n$ is a path on $n$ vertices and $K_{1,m}$ is a star on $m+1$ vertices. In this note, we first give an explicit formula for the path-star Ramsey numbers. Secondly, we study the Ramsey numbers $R(P_n,K_1\\vee F_m)$, where $F_m$ is a linear forest on $m$ vertices. We determine the exact values of $R(P_n,K_1"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1401.3545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-15T11:10:35Z","cross_cats_sorted":[],"title_canon_sha256":"7226d28921ed6afd50219b728f3866189b17e190509632c942840b61448df18c","abstract_canon_sha256":"6c1a2e034fc96ad6d142aa2a08841c148730e1e37a962d15d67db04affdd2b53"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:33.182346Z","signature_b64":"4dCjsJKOi5AOsa4UIv6Tm2cQ30TLccpg8f+ROyTlZB9W81Te+f3Vu+b+ZYw+EHMZZ9R57QpyNTh1aiYmzjkrDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb55c1868c553d1b4211a575de805b226acf76df5f1a6621b2e71f370ba1c5c3","last_reissued_at":"2026-05-18T02:18:33.181805Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:33.181805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On path-quasar Ramsey numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Binlong Li, Bo Ning","submitted_at":"2014-01-15T11:10:35Z","abstract_excerpt":"Let $G_1$ and $G_2$ be two given graphs. 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